Hi, I've been stuck with this problem for a while:
if z=z(x,y), x=x(u,v) and y=y(u,v), prove that this equation is true:
∂u2∂2z=∂x2∂2z(∂u∂x)2+2∂x∂y∂2z∂u∂x∂u∂y+∂y2∂2z(∂u∂y)2+∂x∂z∂u2∂2x+∂y∂z∂u2∂2y
Now, I understand that this is probably just a formula, and I get a result partially, save the part that begins with a 2 (the mixed partial derivative). Could anyone explain where it comes from?
Thank you.
if z=z(x,y), x=x(u,v) and y=y(u,v), prove that this equation is true:
∂u2∂2z=∂x2∂2z(∂u∂x)2+2∂x∂y∂2z∂u∂x∂u∂y+∂y2∂2z(∂u∂y)2+∂x∂z∂u2∂2x+∂y∂z∂u2∂2y
Now, I understand that this is probably just a formula, and I get a result partially, save the part that begins with a 2 (the mixed partial derivative). Could anyone explain where it comes from?
Thank you.
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